5.Aerodynamics of a 2D airfoil NACA 23012 › _files › ...5. Aerodynamics of a 2D airfoil NACA 23012 5.Aerodynamics of a 2D airfoil NACA 23012 5.0.12Description of the case The current

5. Aerodynamics of a 2D airfoil NACA 23012

5. Aerodynamics of a 2D airfoil

NACA 23012

5.0.12 Description of the case

The current chapter studies flow around a 2D airfoil. Although it encompasses the

study of external flow, there are significant differences with Chapter 3, such as the

fact that an airfoil is a streamlined body, and thus the behaviour of the flow around

it changes substantially. Besides the physics of the problem, Chapter 5 includes

new features as the introduction of turbulence models and the creation of a mesh

without using blockMesh.

5.0.13 Hypotheses

• Incompressible flow

• Turbulent flow

• Newtonian flow

• Bidimensional flow ( ∂∂z

= 0)

• Negligible gravitatory effects

• Sea level conditions

• RAS turbulence modelling with wall functions

5.0.14 Physics of the problem

The problem deals with an airfoil NACA 23012 flying at a speed of V = 45 m/s at

sea level. As the medium is air (ν = 1.5× 10−5 m2/s), the Reynolds number is

Re =V c

ν=

45 · 11.5× 10−5

= 3× 106

Jordi Casacuberta Puig 116

OPENFOAM GUIDE FOR BEGINNERS

where c is the chord of the airfoil and is equal to 1 m. The chord is the imaginary

straight line joining the leading and trailing edges. The problem statement is shown

at Figure 5.1.

Figure 5.1: Airfoil NACA 23012 flying at 45 m/s and ambient pressure

The airfoil NACA 23012 has been chosen because of its high aerodynamic perfor-

mance at low flying velocities. It presents a high maximum lift coefficient (Clmax)

and a high stall angle (αstall). Its geometric characteristics are:

• Thickness: 12%

• Maximum thickness position: 30%

• Maximum chamber: 1.83%

• Maximum chamber position: 13%

The shape of the NACA 23012 is shown at Figure 5.2.



Figure 5.2: NACA 23012

In the current chapter there is no easy analytical solution to describe the behaviour

of the fluid. However, it is necessary to keep in mind the main equations and

dimensionless numbers involved in the problem:

The continuity equation,

∇ ·U = 0 (5.1)

The momentum equation,

∂U

∂t+ U · ∇U = −1

ρ∇p + µ

ρ∇2U (5.2)

The Reynolds number,

Re =c|U|ν

(5.3)

The lift coefficient (dimensionless force perpendicular to the flow),

Cl =L

1

2ρ|U|2S

(5.4)

The drag coefficient (dimensionless force parallel to the flow),

Cd =D

1

2ρ|U|2S

(5.5)

The moment coefficient (dimensionless moment of the airfoil calculated at the aero-

dynamic center),

Cm =M

1

2ρ|U|2Sc

(5.6)



For a low velocity flow and a surface with a given rugosity, Cl and Cd depend on

the angle of attack and the Reynolds number:

Cl = f(Re, α) or Cd = f(Re, α)

The angle of attack (α) is the angle between the chord of the airfoil and the direction

of the fluid velocity.

At low values of α, there is a pressure gradient on the upper surface of the airfoil

but it is not strong enough to detach the boundary layer. The flow around the

airfoil is smooth, the drag is low and the lift excellent. The relation between the

lift coefficient and the angle of attack is approximately linear. When α increases,

the pressure gradient grows. Normally, at an angle of attack between 15o and 20o,

the flow is completely detached on the upper surface. When it happens, the airfoil

stalls.

5.0.15 Pre-processing with α = 15o

The following codes contain the information to simulate the case with Re = 3 ×106 using simpleFoam (steady-state solver for incompressible turbulent flow) and

the Spalart-Allmaras turbulence model. As the current case includes new features

and files, a general directory is going to be created with the name AirfoilCase and

containing two files to create the mesh (without using blockMesh), as well as a

subdirectoy containing the cases solved for different angles of attack (2DAirfoil).

Within 2DAirfoil the names of the cases are going to be alpha0 (α = 0o), alpha5 (α =

5o), etc. In particular, the current pre-processing section contains the instructions

to simulate the airfoil for α = 15o (alpha15 case).

5.0.15.1 Mesh generation

As it happened with Chapter 3, the mesh is not going to be uniform. It is neces-

sary to divide the mesh by regions, especially to provide a high refinement to the

walls of the airfoil and downstream. However, in the current case, the geometry

is more complex than a simple circular shape. Therefore, the mesh is going to be

created with GNU Octave and Gmsh Mesh Generator. Then, it will be converted to

OpenFOAM R©.

The first step is to install these two softwares: GNU Octave is a high-level interpreted

language, primarily intended for numerical computations. Gmsh Mesh Generator



contains 4 modules, for geometry description, meshing, solving and post-processing.

They are both free software.

Secondly, it is necessary to create two gedit sheets. The first is going to be named

foilgmsh.m and contains the code shown in the Appendix, Chapter A.

As it can be seen, this code was developed by an external author, who provided it

selflessly. Before the instructions, it is explained how to use it and what parameters

are necessary to define. The code can be entirely found in:

code− saturne.org/forum/old forums files/614676387/foilgmsh.m

Afterwards, a Script is going to be created to execute the previous code and intro-

duce the output to Gmsh Mesh Generator. The results are going to be two new files,

containing the created geometries and mesh. This mesh will be later converted to

the OpenFOAM R© format. The Script must be named executeAirfoilMesher andcontains:

1 #!/ bin /bash

2

3 a r ch i=”naca23012 . dat” #F i l e conta in ing the coo rd ina t e s o f the a i r f o i l ( . dat

ex tens i on )

4 a l f a=15

5 yplus=100

6 e t e r=”a”

7 Re=3000000

8 M=0.128

9 T0=300

10 N=” [100 , 40 , 30 , 30 ] ”

11 bump=1

12 cd /home///A i r f o i lCa s e #I f d i f f e r e n t , wr i t e how to ac c e s s

fo i l gmsh .m

13 octave −−s i l e n t −−eva l ” fo i l gmsh ( ’ $a r ch i ’ , $a l f a , $yplus , ’ $ e t e r ’ , $Re , $M, $T0 ,’$N ’ , $bump) ” #Executes the fo i l gmsh func t i on

14 gmsh −3 naca23012 . dat . geo #Meshes with Gmsh Mesh Generator

So, once the programs have been installed and the gedit sheets containing the pre-

vious codes are ready:

1.- Make the Script executable as it was shown in Section 4.0.11.3

2.- Copy foilgmsh.m and executeAirfoilMesher within AirfoilCase

3.- Copy a file with the coordinates of the airfoil (in this case the NACA 23012)

with the extension .dat named naca23012.dat within AirfoilCase. It can be

easily found in Internet



4.- Access AirfoilCase and type in the terminal:

./executeAirfoilMesher

5.- Select one of the created files (naca23012.dat.msh) and copy it inside an empty

directory named alpha15

6.- Copy a system folder from another case as it is necessary to convert the mesh

to OpenFOAM R© (it does not matter what time-control setting it contains;it will be later correctly defined)

7.- Access 2DAirfoil/alpha15

8.- Type:

gmshToFoam naca23012.dat.msh

9.- The constant directory appears

10.- Acces constant/polyMesh/boundary , change the name of the first patch (symmetry)

to frontAndBack and define it as empty instead of patch (both, type and phys-

icalType). Keep the second name (airfoil) but change its patch type to wall.

Finally, change the third patch name (walls) to topAndBottom and its patch

type to symmetryPlane instead of patch

11.- The mesh is ready

The mesh of the alpha15 case is:



Figure 5.3: Global view of the mesh of the alpha15 case

Figure 5.4: Airfoil shape in the mesh of the alpha15 case



Figure 5.5: Detail of the mesh grading at the walls of the alpha15 case

Advice:

The degree of refinement of the mesh and its relation to the treatment

of the turbulent boundary layer is discussed in Section 5.0.17.2. It de-

termines the value written in the fifth line of executeAirfoilMesher

5.0.15.2 Boundary and initial conditions

Besides the p and U files, as the case is set turbulent, two new files are necessary to be

created. Their names are nut and nuTilda. These dictionaries contain the boundary

conditions of the parameters used to implement the Spalart-Allmaras turbulence

model. Before introducing the user to their calculation, the boundary conditions for

p and U are:

1 /∗−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−∗− C++ −∗−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−∗\2 | ========= | |3 | \\ / F i e l d | OpenFOAM: The Open Source CFD Toolbox |4 | \\ / O pera t i on | Vers ion : 2 . 2 . 1 |5 | \\ / A nd | Web: www.OpenFOAM. org |6 | \\/ M an ipu l a t i on | |7 \∗−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−∗/8 FoamFile

9 {10 ve r s i on 2 . 0 ;

11 format a s c i i ;

12 c l a s s v o l S c a l a rF i e l d ;

13 ob j e c t p ;



14 }15 // ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ //16

17 dimensions [ 0 2 −2 0 0 0 0 ] ;18

19 i n t e r n a l F i e l d uniform 0 ;

20

21 boundaryField

22 {23 i n l e t

24 {25 type f r e e s t r eamPre s su r e ;

26 }27

28 ou t l e t

29 {30 type f r e e s t r eamPre s su r e ;

31 }32

33 a i r f o i l

34 {35 type zeroGradient ;

36 }37

38 frontAndBack

39 {40 type empty ;

41 }42

43 topAndBottom

44 {45 type symmetryPlane ;

46 }47 }48

49 // ∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗ //


9 {10 ve r s i on 2 . 0 ;


12 c l a s s vo lVec to rF i e ld ;

13 ob j e c t U;

14 }15 // ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ //16

17 dimensions [ 0 1 −1 0 0 0 0 ] ;18

19 i n t e r n a l F i e l d uniform (45 0 0) ;



20

21 boundaryField

22 {23 i n l e t

24 {25 type f r e e s t r eam ;

26 f r ees t reamValue uniform (45 0 0) ;

27 }28

29 ou t l e t


32 f r ees t reamValue uniform (45 0 0) ;

33 }34

35 a i r f o i l

36 {37 type f ixedValue ;

38 value uniform (0 0 0) ;

39 }40

41 frontAndBack

42 {43 type empty ;

44 }45

46 topAndBottom


49 }50 }51

52 // ∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗ //

The dictionaries for nut and nuTilda (they must be saved within 0 with these names)

are:


9 {10 ve r s i on 2 . 0 ;



13 ob j e c t nut ;

14 }15 // ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ //16

17 dimensions [ 0 2 −1 0 0 0 0 ] ;18



19 i n t e r n a l F i e l d uniform 0 . 0386 ;

20

21 boundaryField

22 {23 i n l e t


26 f r ees t reamValue uniform 0 . 0386 ;

27 }28

29 ou t l e t



33 }34

35 a i r f o i l

36 {37 type nutUSpaldingWallFunction ;

38 value uniform 0 ;

39 }40

41 frontAndBack

42 {43 type empty ;

44 }45

46 topAndBottom


49 }50 }51

52 // ∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗ //


9 {10 ve r s i on 2 . 0 ;



13 ob j e c t nuTilda ;

14 }15 // ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ //16

17 dimensions [ 0 2 −1 0 0 0 0 ] ;18

19 i n t e r n a l F i e l d uniform 0 . 1929 ;

20

21 boundaryField



22 {23 i n l e t



27 }28

29 ou t l e t



33 }34

35 a i r f o i l

36 {37 type f ixedValue ;

38 value uniform 0 ;

39 }40

41 frontAndBack

42 {43 type empty ;

44 }45

46 topAndBottom


49 }50 }51

52 // ∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗ //

νt (nut) and ν̃t (nuTilda) are parameters required to simulate the case with a turbu-

lence model (as it was said, for this case it is used the Spalart-Allmaras one-equation

model). Mathematically, they are determined as:

ν̃t =

√3

2(|U|Il) (5.7)

where |U| is the mean flow velocity, I is the turbulence intensity and l is the tur-bulent length scale. They can be computed as:

I ≈ 5%

l ≈ 0.07 · c = 0.07



With these assumptions, ν̃t = 0.1929. Then, a convenient option is to set ν̃t = 5νt

in the freestream. The model then provides fully turbulent results and any regions

like boundary layers that contain shear become fully turbulent.

5.0.15.3 Physical properties


9 {10 ve r s i on 2 . 0 ;


12 c l a s s d i c t i ona ry ;

13 l o c a t i o n ” constant ” ;

14 ob j e c t t r an spo r tP rope r t i e s ;

15 }16 // ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ //17

18 transportModel Newtonian ;

19

20 rho rho [ 1 −3 0 0 0 0 0 ] 1 . 2 2 5 ;21

22 nu nu [ 0 2 −1 0 0 0 0 ] 1 . 5 e−05;23

24 CrossPowerLawCoeffs

25 {26 nu0 nu0 [ 0 2 −1 0 0 0 0 ] 1e−06;27 nuInf nuInf [ 0 2 −1 0 0 0 0 ] 1e−06;28 m m [ 0 0 1 0 0 0 0 ] 1 ;

29 n n [ 0 0 0 0 0 0 0 ] 1 ;

30 }31

32 BirdCarreauCoef f s

33 {34 nu0 nu0 [ 0 2 −1 0 0 0 0 ] 1e−06;35 nuInf nuInf [ 0 2 −1 0 0 0 0 ] 1e−06;36 k k [ 0 0 1 0 0 0 0 ] 0 ;

37 n n [ 0 0 0 0 0 0 0 ] 1 ;

38 }39

40 // ∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗ //

1 /∗−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−∗− C++ −∗−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−∗\2 | ========= | |3 | \\ / F i e l d | OpenFOAM: The Open Source CFD Toolbox |4 | \\ / O pera t i on | Vers ion : 2 . 2 . 1 |5 | \\ / A nd | Web: www.OpenFOAM. org |6 | \\/ M an ipu l a t i on | |



7 \∗−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−∗/8 FoamFile

9 {10 ve r s i on 2 . 0 ;



13 l o c a t i o n ” constant ” ;

14 ob j e c t RASProperties ;

15 }16 // ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ //17

18 RASModel Spa lartAl lmaras ;

19

20 turbu lence on ;

21

22 p r i n tCoe f f s on ;

23

24 // ∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗ //

5.0.15.4 Control


9 {10 ve r s i on 2 . 0 ;



13 l o c a t i o n ” system” ;

14 ob j e c t con t r o lD i c t ;

15 }16 // ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ //17

18 app l i c a t i on simpleFoam ;

19

20 startFrom startTime ;

21

22 startTime 0 ;

23

24 stopAt endTime ;

25

26 endTime 10000 ;

27

28 deltaT 1 ;

29

30 wr i teContro l t imeStep ;

31

32 wr i t e I n t e r v a l 100 ;

33

34 purgeWrite 0 ;



35

36 writeFormat a s c i i ;

37

38 wr i t eP r e c i s i o n 7 ;

39

40 writeCompress ion o f f ;

41

42 timeFormat gene ra l ;

43

44 t imePrec i s i on 6 ;

45

46 runTimeModif iable t rue ;

47

48 f un c t i on s

49 (

50 f o r c e s

51 {52 type f o r c e s ;

53 func t i onObjec tL ibs ( ” l i b f o r c e s . so ” ) ;

54 patches ( a i r f o i l ) ;

55 pName p ;

56 UName U;

57 rhoName rho In f ;

58 rho In f 1 . 2 2 5 ;

59 CofR (0 .2704 −0.0012 4 .0128) ;60 outputControl t imeStep ;

61 output In t e rva l 100 ;

62 }63 f o r c eCo e f f s

64 {65 type f o r c eCo e f f s ;

66 func t i onObjec tL ibs ( ” l i b f o r c e s . so ” ) ;

67 patches ( a i r f o i l ) ;

68 pName p ;

69 UName U;

70 rhoName rho In f ;

71 rho In f 1 . 2 2 5 ;

72 CofR (0 .2704 −0.0012 4 .0128) ;73 l i f t D i r (0 1 0) ;

74 dragDir (1 0 0) ;

75 pi tchAxi s (0 0 1) ;

76 magUInf 45 ; //

77 lRe f 1 ; //

78 Aref 0 . 1 ; //

79 outputControl t imeStep ;

80 output In t e rva l 100 ;

81 }82 ) ;

83

84 // ∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗ //

5.0.15.5 Discretization and linear-solver settings

1 /∗−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−∗− C++ −∗−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−∗\2 | ========= | |



3 | \\ / F i e l d | OpenFOAM: The Open Source CFD Toolbox |4 | \\ / O pera t i on | Vers ion : 2 . 2 . 1 |5 | \\ / A nd | Web: www.OpenFOAM. org |6 | \\/ M an ipu l a t i on | |7 \∗−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−∗/8 FoamFile

9 {10 ve r s i on 2 . 0 ;




14 ob j e c t fvSchemes ;

15 }16 // ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ //17

18 ddtSchemes

19 {20 de f au l t s t eadyState ;

21 }22

23 gradSchemes

24 {25 de f au l t Gauss l i n e a r ;

26 grad (p) Gauss l i n e a r ;

27 grad (U) Gauss l i n e a r ;

28 }29

30 divSchemes

31 {32 de f au l t none ;

33 div ( phi ,U) Gauss l inearUpwind grad (U) ;

34 div ( phi , nuTilda ) Gauss l inearUpwind grad ( nuTilda ) ;

35 div ( ( nuEff∗dev (T( grad (U) ) ) ) ) Gauss l i n e a r ;36 }37 l ap lac ianSchemes

38 {39 de f au l t none ;

40 l a p l a c i a n ( nuEff ,U) Gauss l i n e a r co r r e c t ed ;

41 l a p l a c i a n ( ( 1 |A(U) ) ,p) Gauss l i n e a r co r r e c t ed ;42 l a p l a c i a n ( DnuTildaEff , nuTilda ) Gauss l i n e a r co r r e c t ed ;

43 l a p l a c i a n (1 , p) Gauss l i n e a r co r r e c t ed ;

44 }45 i n t e rpo la t i onSchemes

46 {47 de f au l t l i n e a r ;

48 i n t e r p o l a t e (U) l i n e a r ;

49 }50

51 snGradSchemes

52 {53 de f au l t c o r r e c t ed ;

54 }55

56 f luxRequ i red

57 {58 de f au l t no ;

59 p ;



60 }61

62 // ∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗ //


9 {10 ve r s i on 2 . 0 ;




14 ob j e c t f vSo lu t i on ;

15 }16 // ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ //17

18 s o l v e r s

19 {20 p

21 {22 s o l v e r GAMG;

23 t o l e r an c e 1e−06;24 r e lTo l 0 . 1 ;

25 smoother GaussSe ide l ;

26 nPreSweeps 0 ;

27 nPostSweeps 2 ;

28 cacheAgglomeration true ;

29 nCe l l s InCoar s e s tLeve l 10 ;

30 agglomerator faceAreaPai r ;

31 mergeLevels 1 ;

32 }33

34 U

35 {36 s o l v e r smoothSolver ;


38 nSweeps 2 ;


41 }42

43 nuTilda

44 {45 s o l v e r smoothSolver ;


47 nSweeps 2 ;


50 }51 }52



53 SIMPLE

54 {55 nCorrector s 1 ;

56 nNonOrthogonalCorrectors 2 ;

57 pRefCel l 0 ;

58 pRefValue 0 ;

59 r e s i dua lCon t r o l

60 {61 p 1e−5;62 U 1e−5;63 nuTilda 1e−5;64 }65 }66 r e l axa t i onFac t o r s

67 {68

69 f i e l d s

70 {71 p 0 . 3 ;

72 }73 equat ions

74 {75 U 0 . 7 ;

76 nuTilda 0 . 7 ;

77 }78 }79

80 // ∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗ //

At the end of the pre-processing, the structure of directories, subdirectories and files

within alpha15 should be as follows:



alpha15

0

p

U

νt

ν̃t

constant

polyMesh

transportProperties

RASProperties

system

controlDict

fvSchemes

fvSolutions

naca23012.dat.msh

5.0.16 Post-processing

5.0.16.1 Results of the simulation for α = 15o

The velocity field:

Figure 5.6: Velocity field around the NACA 23012 at α = 15o (m/s)

The pressure field:



Figure 5.7: Pressure field around the NACA 23012 at α = 15o (m2/s2)

The streamlines around the airfoil:

Figure 5.8: Streamlines around the NACA 23012 at α = 15o (m/s)

It is possible to observe that at α = 15o the flow has started to detach due to the

strong pressure gradient on the upper surface. However, 15o is not the maximum

angle of attack (αstall) because the fluid is not fully detached and therefore stall has

not yet happened.

The vector field at the trailing edge (to appreciate the boundary layer detachment):



Figure 5.9: Velocity vectors around the NACA 23012 at α = 15o (m/s)

The distribution of ν̃t in the domain:

Figure 5.10: Distribution of ν̃t in the domain of the alpha15 case

As it was explained in Chapter 3, the plot of the aerodynamic forces in front of

the time gives information about the convergence of the case. In Figure 5.11 it is

represented the lift coefficient:



Figure 5.11: Evolution of the lift coefficient (ordinate axis) with the time (abscissaaxis) in the alpha15 case

As it can be seen, the case has converged rapidly.

5.0.16.2 Results of the simulation for a range of α. Plot of the main

aerodynamic curves

To simulate the NACA 23012 for different configurations (according to α), it is nec-

essary to change this parameter before meshing. It has to be done in the parameter

definition within executeAirfoilMesher . At the fourth line of the Script, the user can

write the angle of attack (in degrees) at which the simulation will be carried out.

Caution:

For α > 15o, as the flow detaches, there are unsteady phenomena. Thus,

simpleFoam would not be the appropriate solver for these cases

Caution:

Although the angle of attack changes from one case to the other, the

velocity boundary conditions have to be set equal for all cases. This is

because the flow velocity is not modified, but the geometric characteris-

tics of the airfoil shape in the mesh

Some representative results of the behaviour of the NACA 23012 for different con-

figurations are:



Figure 5.12: Behaviour of the flow around the NACA 23012 at α = 0o (m/s)





By using these simulations, the main aerodynamic curves have been plot (in a range

between −10o and 15o with intervals of 5o). It can be done by copying the Cland Cd obtained with the simulations and plot their relation using Gnuplot and the

instructions shown in Section 3.6.3. The curves are:

Figure 5.15: Relation between Cl (ordinate axis) and α (abscissa axis) for the NACA23012



Figure 5.16: Relation between Cl (ordinate axis) and Cd (abscissa axis), polar curve,for the NACA 23012

It can be seen that for near zero angles of attack, the relation between Cl and α is

linear. However, it is shown that this trend starts to stabilize when high values of

|α| are achieved due to the boundary layer detachment.

5.0.17 Additional utilities

5.0.17.1 Mesh conversion

The user can generate meshes using other packages and convert them into the format

that OpenFOAM R© uses. This has been done in Section 5.0.15.1 to convert a meshexported from Gmsh Mesh Generator by typing:

gmshToFoam

Furthermore, it is possible to convert meshes exported from other packages using

instructions such as:

ansysToFoam

fluentMeshToFoam



5.0.17.2 Computation of y+

y+ is the dimensionless wall distance for a wall-bounded flow. It can be expressed

as:

y+ =u?y

ν(5.8)

where u? is the friction velocity

(u? ≡

√τwρ

), y is the distance to the nearest wall

and ν is the kinematic viscosity of the fluid. y+ is commonly used in boundary layer

theory and in defining the law of the wall.

y+ plays a relevant role in the treatment of the boundary layer. The subdivision

of the near-wall region in a turbulent boundary layer can be summarized as follows

(Fluent, 2005 ):

• y+ < 5: viscous sublayer region (velocity profile is assumed to be laminar andviscous stress dominates the wall shear)

• 5 < y+ < 30: buffer region (both viscous and turbulent shear dominate)

• 30 < y+ < 300: fully turbulent portion or log-law region (turbulent shearpredominates)

In the alpha15 case, a wall function has been used to model the behaviour of the

boundary layer. To use a wall function approach for a particular turbulence model

with confidence, it is necessary to ensure that the y+ values are within a certain

range. As in the current case a RAS model has been implemented, it is necessary

to guarantee that the first node of the mesh falls within the log-law region. It is to

ensure that 30 < y+ < 300.

Caution:

In addition to the concern about having a mesh with y+ values that are

too large, it is necessary to be aware that if the y+ is too low then the

first calculation point will be placed in the viscous sublayer region and

the wall function will also be outside its validity

Caution:

If an attached flow is modeled, then generally a wall function approach

can be used. If flow separation is expected and the accurate prediction



of the separation point will have an impact on the results then it would

be advisable to resolve the boundary layer with a finer mesh

OpenFOAM R© presents a utility to calculate and report y+ for all the wall patches.Note that as it depends on the local Reynolds number, it can only be obtained in

the post-processing. Consequently only approximate values can be estimated when

meshing.

As in the current case a RAS turbulence model has been used, the instruction

(written in the terminal) to obtain y+ is:

yPlusRAS

To view the results with ParaView it is necessary to select the yPlus box located

within Volume Fields, choose the time at which the results will be consulted and

select the wall patch (airfoil). The results:

Figure 5.17: Distribution of y+ at the wall of the airfoil in the alpha15 case att = 10000 s

Note that there are some regions where y+ is not within the required range. As it

can be seen, it is basically located in the region of boundary layer detachment. In

these regions the wall function approach would be out of its validity.



5.0.17.3 Isobars around a body

In this section it is explained how to create a contour plot across a plane. It will be

used to plot the isobars around the NACA 23012 at α = 15o.

First of all the user has to launch ParaView, click on internalMesh and select the

pressure field. Then, with the alpha15.OpenFOAM module highlighted, go to Filters

-> Alphabetical -> Slice. The Slice filter allows the user to specify a cutting plane

making the case truly two-dimensional. For the current case click on Z Normal so the

plane will cut the domain in the adequate direction. Afterwards, select the Slice1

module and go to Filters -> Alphabetical -> Contour.

To appreciate the isobars, select the Slice1 and Contour1 modules while keeping

alpha15.OpenFOAM deselected. In the Properties menu of the Contour module, select

the pressure field in the Contour By option and in the Isosurface panel click on New

Range. Make sure that the From and To values coincide with the maximum and

minimum of the legend and set the Steps option to 25. Finally, go to the Display

menu and in the Color panel choose Solid Color in Color by instead of the pressure.

Choose a color of your choice to represent the isobars. The results are then:

Figure 5.18: Isobars around the NACA 23012 at the alpha15 case at t = 10000 s(m2/s2)

5.0.17.4 Tube-like streamlines

In Section 2.6.2 it was shown how to plot the streamlines. Additionally, in the cur-

rent section it is explained how to represent tube-like streamlines. It may add more



realism to the simulation or simply a different way of representing the streamlines.

The differences between both configurations can be observed in the following figures:

Figure 5.19: Streamlines around the NACA 23012 at the alpha15 case at t = 10000s (m/s)

Figure 5.20: Tube-like streamlines around the NACA 23012 at the alpha15 case att = 10000 s (m/s)

To obtain a configuration like Figure 5.20 it is first necessary to plot the streamlines

as it was shown in Section 2.6.2. In the current case, Number of Points has been set

to 3000 and Radius to 2. Once it is generated, it is necessary to select the module of

the streamlines and go to Filters -> Alphabetical -> Tube. Finally, the thickness of

the tube-like streamlines can be adjusted by changing the Radius option. In Figure

5.20 this parameter has been set to 0.01.


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